Master in Geogebra for Mathematics

Explore basic geometric elements by creating points and lines in GeoGebra, observe coordinates, join points to objects, and construct segments, rays, and polygons with intersections and vectors.

Learn the difference between independent and dependent points in geogebra, how dependent points move with their objects, and how the algebraic view sorts elements by construction and dependency.

Explore line constructions in GeoGebra, including perpendicular and parallel lines, perpendicular bisectors, angle bisectors, tangents, polar or diameter lines, best fit lines, and locus.

Geogebra polygon tools to draw regular and irregular polygons from vertices, return to origin, and manage color and properties; learn rigid and vector polygon behaviors.

Explore the circle and arcs toolbar to generate circles, semicircles, arcs, and circular sectors. Create with center-radius, two-point compass, three-point circle, and various semicircular and circumcircular options.

Learn how to construct tangents to circumferences in geogebra, including tangents from external points, tangents to arcs, and line construction options such as perpendicular, parallel, bisector, tangents, and polar.

Learn to measure angles in GeoGebra using the measurements toolbar, selecting lines or points, choosing counterclockwise or clockwise direction, and also measure distance, circumference, area, and slope.

Learn to obtain the area and perimeter of a regular six-sided polygon using the measurement tool, with area found by clicking inside and sides measured by distance or longitude.

Explore changing properties of points, lines, polygons, and circular sectors in Geogebra, including color, style, labels, and opacity, plus configuring graphics and applying patterns.

Explore conic curves with Geogebra, focusing on the ellipse: construct the ellipse, view its center, vertices, axis, and eccentricity, and verify the constant sum of distances to the foci.

Explore constructing a parabola in GeoGebra by defining a focus and directrix, using the parabola tool, and verifying the focus-directrix distance property.

Explore constructing and analyzing a hyperbola in Geogebra by algebraic equation and graphical methods, identifying vertices, center, axes, eccentricity, and using the five-point tool to fit through points.

Explore dynamic geometry transformations in GeoGebra, including reflection about lines, points, and circles, rotation around a point, and translations by vectors, plus scaling by a center and factor.

Insert images in GeoGebra using the insert image option to add jpg file to a function or geometry file, place and resize with corner points, and apply images inside polygons.

Master the inserting text features in GeoGebra by adding labels to polygons, using dynamic coordinates and values like area and length, and formatting options like color, bold, italics, and sizes.

Explore how the construction protocol displays the step-by-step process of building figures, such as circles and flower patterns, with both graphic and algebraic views, and adjustable element order.

Graph functions in GeoGebra using the graphing view with the Cartesian plane and grid. Enter x-based expressions to visualize quadratics and polynomials, then adjust zoom, names, grid, and line style.

Explore special points of functions in Geogebra, including maxima, minima, inflection points, and axis intersections for linear, quadratic, and cubic functions, with interactive point labeling and value checks.

Explore exponential and logarithmic functions by graphing with bases such as 2, 10, and e, and using the function keyboard to set bases and exponents.

Learn to differentiate polynomials and explore derivatives graphically and algebraically, then integrate to compute areas under curves with definite bounds.

Use sliders to analyze functions, adjusting coefficients like a and b in x^2 + b x to see how the graph moves, and explore exponential and other functions with sliders.

Set the x axis to pi to match the 1pi, 2pi, 3pi intervals. Then graph the six basic trigonometric functions—sine, cosine, tangent—and their inverses like arcsin, arccos, and arctan.

Explore how to view a trigonometrical function in a partial domain, such as 0 to 2π, by restricting to a segment and identifying roots, intersections, and undefined points in GeoGebra.

Explore the new 3d graphics view in GeoGebra, mastering axes, planes, and perspective options. Extrude polygons to 3d solids and measure volume with the updated tools.

Learn to draw 3d solids using GeoGebra solid tools. Create pyramids, prisms, cones, and cubes by setting base, apex, altitude, height, with extrusion and color adjustments.

Explore polyhedrons and nets in GeoGebra by building prisms, cubes, and pyramids, and generating their nets. Observe top, side, and back views to understand the development of solids.

Explore GeoGebra CAS for algebra and calculus, visualize linear expressions as lines, and calculate, factor, and integrate to solve equations with exact or decimal values.

Explore the spreadsheet view in Geogebra to create points, tables, and polylines, link algebra and graphics, and analyze x–y values with animated point displays.

Explore GeoGebra for mathematics to create statistics graphics, including bar charts, box plots, and frequency tables, then analyze one- and two-variable data with regression and t tests, exporting visuals.

Explore a new augmented reality app for geometry and math on mobile devices, available in the Apple store, with examples to download, try, and watch on George Yarbrough's YouTube channel.